Need Help? has been used in asphalt cement to 112.3 97.0 92.7 86.0 102.0 99,2 95

Question

Need Help? has been used in asphalt cement to 112.3 97.0 92.7 86.0 102.0 99,2 95.8 103.5 89.0 86.7 (MPa) on x cube st 59.8 581 49.0 Interpret the slope 0 A on·MPs rease in axial strength is associated with an increase in the predicted obe strength al to slope. A one MPa increase in axcial strength is associated with an increase in the predicted cube strength equal to the slope. 0 A one MPa increase in cube strength is associated with an increase in the predicted axial strength equal to the slope. 0 A one MPa decrease in cube strength is associated with an increase in the predicted axial streng equal to the slope. The coefficient of determination is the number of the observed samples of axial strength of asphalt that can be explained by varlation in cibe strengh O The coefficient of 0 The coefficient of determination is the number of the observed samples of al strength of asphalk that cannot be explained by variation in coubé strength is the proportion of the observed variation in axilal strength of asphalt samples of this type that can be atvributed to its linear relationship with cube strangth The ceffiient of determination is the proportion of the observed variation in axial strength of asphait samples of this type that cannot be attributed to its linear relationship with cube strangth an estimate of the error standard deviation n the simple brew regression model.(Round your answer to three decimal places.) interpret tho ostmate orthe error standard deviation in "e simpl·Inear regression model. O The models prediction for aal strength wil typically differ from the spedmen's actual axial strength by an amount greater than one errer standard deviatien th·moder, preditior, fo' aiitrength w. typicaly dner from the spilinen's actual alal strength by an amount greater than two error standard deviations. The model's prediction for asial strength will typically iffer from the spedmen's actual axial strength by an amount within two rror standard devianions. The model's prediction for axial strength will typically differ from the specmen's actual axial strength by an amount within one error standard deviatien

Explanation / Answer

We have excel output for regression :

Intercept = a = -31.3795, slope = b= 0.9842

Hence the regression equation is

y = -31.3795 + 0.9842 x

Interpretation of slope : A one MPa increases in cube strength is associated with an increase in the predicted axial strength equal to the slope.

b) The coefficient of determination = R2 = 0.6359

Interpretation : The coefficient of determination is the proportion of observed variation in axial strength of asphalt samples of this type that can be attributed to its linear relationship with cube strength.

c) Standard error = Se = 6.524

The model's prediction for axial strength will typically differ from the speciman's actual axial strength by an amount greater than two error standard deviations.

SUMMARY OUTPUT Regression Statistics Multiple R 0.797417 R Square 0.635874 Adjusted R Square 0.590358 Standard Error 6.524065 Observations 10 ANOVA df SS MS F Significance F Regression 1 594.6287 594.6287 13.97042 0.005724 Residual 8 340.5073 42.56342 Total 9 935.136 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept -31.3795 25.47348 -1.23185 0.252983 -90.1214 27.36246 x 0.98423 0.263325 3.737702 0.005724 0.377002 1.591459

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